Understanding Performance Tradeoffs in Algorithms for Solving Oversubscribed Scheduling

In recent years, planning and scheduling research has paid increasing attention to problems that involve resource oversubscription, where cumulative demand for resources outstrips their availability and some subset of goals or tasks must be excluded. Two basic classes of techniques to solve oversubscribed scheduling problems have emerged: searching directly in the space of possible schedules and searching in an alternative space of task permutations (by relying on a schedule builder to provide a mapping to schedule space). In some problem contexts, permutation-based search methods have been shown to outperform schedule-space search methods, while in others the opposite has been shown to be the case. We consider two techniques for which this behavior has been observed: TaskSwap (TS), a schedule-space repair search procedure, and Squeaky Wheel Optimization (SWO), a permutation-space scheduling procedure. We analyze the circumstances under which one can be expected to dominate the other. Starting from a real-world scheduling problem where SWO has been shown to outperform TS, we construct a series of problem instances that increasingly incorporate characteristics of a second real-world scheduling problem, where TS has been found to outperform SWO. Experimental results provide insights into when schedule-space methods and permutation-based methods may be most appropriate. Introduction and Motivation As research in automated planning and scheduling has moved into problem domains that more accurately model real-world concerns, one issue that has garnered increasing interest has been that of oversubscription (Kramer & Smith 2004; Barbulescu et al. 2006; Smith 2004; Nigenda & Kambhampati 2005). Generally speaking, an oversubscribed problem is one in which the resources available (e.g., time, capacity) are not sufficient to permit accomplishment of all stated tasks or goals, and hence the problem solver must decide which subset of tasks or goals to carry out. The basic objective is to maximize the number of tasks accommodated or goals satisfied, subject in some cases to associated task or goal priorities. Oversubscribed problems arise in a broad range of application domains, including rover task planning (Smith 2004; Joslin et al. 2005), satellite and telescope scheduling (Bresina 1996; Copyright c © 2007, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Frank et al. 2001; Barbulescu et al. 2006) and military airlift allocation (Kramer & Smith 2004). With respect to solving oversubscribed scheduling problems, two basic classes of solution techniques have emerged: those that search directly in the space of possible schedules, and those that search in an alternative space of task permutations (in which case a schedule builder is used to provide a mapping to schedule space). Both permutation-space and schedule-space methods have been shown to perform effectively in specific problem domains. This raises the question of whether there are problem characteristics that might suggest the appropriateness of one over the other. In this paper, we attempt to gain insight into this general question by analyzing the performance tradeoffs between two specific methods on a common set of problem instances. Our starting point is two oversubscribed scheduling problems that are quite similar in character, the USAF Satellite Control Network (AFSCN) problem previously studied in (Barbulescu et al. 2006) and the USAF Air Mobility Command (AMC) airlift scheduling problem described in (Kramer & Smith 2005a). Prior research with the AFSCN problem has shown permutation-space scheduling procedures such as Squeaky Wheel Optimization (SWO) to dominate schedule-space methods. Other prior work (Kramer & Smith 2004; 2005b) has demonstrated the effectiveness of a schedule-space method called TaskSwap (TS) in solving the AMC scheduling problem, and in fact TS can be shown to outperform SWO in this domain. Given these results, we attempt to understand what problem characteristics set these domains and solution techniques apart. We define a series of problem sets which generalize from the AFSCN problem and increasingly incorporate characteristics of the AMC problem. Our experimental results indicate that problem hardness and the presence or absence of task priorities are two distinguishing performance factors. Before describing the AFSCN and AMC domains and presenting our experimental analysis, we briefly summarize prior approaches to oversubscribed scheduling problems and the two specific methods of interest to our study. Permutation Space vs. Schedule Space Search As indicated above, we can distinguish two basic classes of approaches to solving oversubscribed scheduling problems based on the search space representation that is used.